Lasers that emit light at a stable frequency with a narrow linewidth can find applications in a variety of areas. For example, next generation atomic clocks based on optical rather than microwave transitions can benefit from stable laser sources that can accurately probe the sub-Hertz linewidths available in laser-cooled samples. Laser systems with narrow linewidths and low frequency and amplitude noise may also help the search for gravitational waves (e.g., Advanced LIGO) by providing a stable phase reference.
The linewidth of an unstabilized or “free-running” laser, which is related to the short-term (e.g., less than millisecond) stability, is often too large for such high-precision applications. Linewidths of free-running lasers can be a few kilohertz, which is far above the Schawlow-Townes limit, a quantum limit for the linewidth of a laser. Various sources of technical noise, including but not limited to fluctuations of the resonator length, the pump power, and the temperature of the laser, can contribute to increased linewidth. Semiconductor lasers, which are widely utilized in fields spanning engineering, biology, chemistry, and medicine, may have linewidths in the megahertz range, and the linewidths can increase above the Schawlow-Townes limit by amplitude-phase coupling or charge carrier fluctuations.
To stabilize the frequency of a laser, an external passive cavity with a set of resonant frequencies can be used. The laser frequency can be compared to a resonant frequency of the cavity in real-time and, using a feedback loop, the laser frequency can be adjusted when the two frequencies are not equal. At present, however, there are no electronics fast enough to measure such a frequency difference directly. Instead, the frequency difference information is typically extracted from other signals for laser frequency stabilization.
One way to stabilize a laser frequency is the Pound-Drever-Hall (PDH) locking technique, in which a portion of the output light from a laser source is phase modulated and sent to an external cavity that has a set of resonant frequencies. The reflected beam from the external cavity contains information about the difference between the laser frequency and a cavity resonant frequency. This information can be extracted by mixing the reflected beam power signal with the drive signal for the phase modulation and feeding the resulting beat signal into a servo to appropriately adjust the laser frequency. In this way, the laser frequency can be locked to the resonant frequency of the external cavity. PDH locking is widely used, but the bandwidth of the feedback is intrinsically limited by the modulation frequency. Because high speed modulators are generally expensive, the overall apparatus for high-performance frequency stabilization using PDH locking can be costly.
Another technique for laser frequency stabilization is Hansch-Couillaud (HC) locking, which uses polarization spectroscopy in connection with an external cavity. The external cavity contains a polarizer, which allows only one polarization mode to resonate in the cavity. In HC locking, the cavity is positioned to receive a laser beam linearly polarized at an angle with respect to the polarizer axis so that one polarization component of the light is directly reflected as a reference, while the other polarization component enters the cavity and passes through the polarizer in the cavity. The resonant polarization component experiences a frequency-dependent phase change relative to the polarization component used as a reference, creating an elliptically polarized reflected beam. The phase change can then be detected by a polarization analyzer whose output indicates the amount of frequency deviation from the cavity resonance and can provide an error signal for frequency stabilization. Although free of modulation, the HC method suffers from other drawbacks. For example, the intracavity polarizer introduces losses even for light polarized along its polarization axis.